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3 years ago

20% of__= 3???????????????????????????????????????????????

Mathematics

2 answers:

svetlana [45]3 years ago

8 0

20% = 0.2
20 * 5 = 100%
3 * 5 = 15
20% of 15 = 3

Hope this helps!

maw [93]3 years ago

5 0

20% = 1/5 of 100%

3 is 1/5 of ____

3 * 5 = 15

3 is 1/5 of 15
3 is 20% of 15

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The length of the short side is 14.5 units, the length of the other short side is 18.5 units, and the length of the longest side is 23.5 units.

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The Pythagorean Theorem

<em> If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. </em>

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Applying the Pythagorean Theorem to find the lengths of the three sides we get:

$(x)^2+(x+4)^2=(x+9)^2\\\\2x^2+8x+16=x^2+18x+81\\\\2x^2+8x-65=x^2+18x\\\\2x^2-10x-65=x^2\\\\x^2-10x-65=0$

Solve with the quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-10,\:c=-65:\quad x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}\\\\x_{1}=\frac{-\left(-10\right)+ \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5+3\sqrt{10}\\\\x_{2}=\frac{-\left(-10\right)- \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5-3\sqrt{10}$

Because a length can only be positive, the only solution is

$x=5+3\sqrt{10}\approx 14.5$

The length of the short side is 14.5, the length of the other short side is $14.5+4=18.5$ , and the length of the longest side is $14.5+9=23.5$ .

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